The study includes n=30 subjects with T2D. All study participants will be provided all meals for both the low carbohydrate diet and the control diet for free in the first part of the study, i.e. week 0 to 12, and these food items will be prepared and distributed from the research kitchen of the Department of Nutrition, Exercise and Sports, Faculty of Science, University of Copenhagen, Denmark to optimize compliance and adherence to the prescriped diet. During the isoenergetic diet study weight stability is reinforced to facilitate interpretation of the diet effect. All diets will be isoenergetic in accordance with the participant's estimated daily total energy expenditure (TEE). A dual energy X-ray absorptiometry (DXA) scan will be undertaken to determine body composition for each participant in order to estimate daily resting energy expenditure (REE). To estimate TEE, physical activity level expressed as PAL = TEE / REE, will be estimated. If a participant develops weight loss or weight gain at three consecutive measurements and/or lose or gain > 1kg of weight compared to baseline, the amount of energy in the diet wil be adjusted accordingly to enforce weight stability throughout the full duration of the study.